Rather than follow LTC's lead Doge is slowly following Coinye's lead - the community support cannot overcome the inertia of miners dumping the coin for minimal profits. Any rise in price is met with a few miners throwing ASICs at it for a couple hours and dumping.
Coinye was destroyed by a lawsuit. It seems more likely that Dogecoin is just suffering from a downtrend that's affecting all of the older more established altcoins (of which DOGE was probably the last). Both Peercoin and Litecoin have been experiencing the same decline for most of the year too as attention has shifted to the newer altcoins (of which NXT was probably the first and includes coins like DRK, XMR, etc.) which have popped up in recent months.
This can probably be moved to the alt coin section. IMO dogecoin won't ever come close to BTC prices. I don't think the devs even intend on that. I guess anything is possible, but very very improbable
Assuming BTC price of $1,000 for simplicity, if each DOGE was worth $1,000 then Dogecoin at its current state would need to have a market cap of $90 trillion. So yes, it would be very, very improbable.